Finite Group Databasebeta

← C11×#9101 #14586294

Subgroups — C11×#9101 #14586294

Order 2816.

630 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2972C211yesmaximal, characteristic, complemented
2C11×#2328C211yesmaximal, characteristic
3C11×#1478C212yesmaximal, complemented
4C11×#1460C211yesmaximal, characteristic, complemented
5C11×#1274C212yesmaximal, complemented
6C2×C11×#127C411yescharacteristic
7C2×C4×D4×C11C2211yescharacteristic
8C2×C4×D4×C11C2211yescharacteristic
9C8×D4×C11—24no—
10C11×#431C2212yes—
11C11×#431C2212yes—
12C2×C11×C22⋊C8—22no—
13C11×#390C411yescharacteristic
14C11×#390C411yescharacteristic
15C11×#386—22no—
16C11×#386—22no—
17C11×#382C411yescharacteristic
18C11×#376C2211yescharacteristic
19C11×D4⋊C8—24no—
20C11×#323—22no—
21C22×D4×C11—22no—
22C22×D4×C11C2×C411yescharacteristic
23C22×D4×C11C2×C411yescharacteristic
24C23×C4×C11—21no—
25C23×C4×C11D412yes—
26C22×C8×C11—24no—
27C11×#127—22no—
28C11×#127C814yescomplemented
29C4×D4×C11—22no—
30C4×D4×C11—22no—
31C4×D4×C11—22no—
32C4×D4×C11—22no—
33C2×C11×C4⋊C4C2×C411yescharacteristic
34C2×C11×C4⋊C4C2×C411yescharacteristic
35C2×C11×C22⋊C4—21no—
36C2×C11×C22⋊C4—22no—
37C2×C11×C22⋊C4—22no—
38C2×C11×C22⋊C4D412yes—
39C2×C42×C11C2×C411yescharacteristic
40C2×C42×C11C2×C411yescharacteristic
41C2×C42×C11C2311yescharacteristic
42C11×C4⋊C8—22no—
43C11×C4⋊C8—22no—
44C11×C22⋊C8—24no—
45C11×C22⋊C8—22no—
46C11×C22⋊C8—22no—
47C4×C8×C11—22no—
48C4×C8×C11D414yescomplemented
49C11×#95—22no—
50C11×#95—21no—
51C11×#95—21no—
52#9101C1111yesmaximal, characteristic, direct product factor, Sylow
53C24×C11—21no—
54C24×C11C22⋊C412yes—
55C2×D4×C11—28no—
56C2×D4×C11—22no—
57C2×D4×C11—22no—
58C2×D4×C11—21no—
59C2×D4×C11—22no—
60C2×D4×C11—22no—
61C2×D4×C11—82no—
62C2×D4×C11—82no—
63C2×D4×C11C2×C812yes—
64C2×D4×C11C2×C812yescomplemented
65C2×D4×C11M1612yes—
66C22×C4×C11—21no—
67C22×C4×C11—22no—
68C22×C4×C11—22no—
69C22×C4×C11—21no—
70C22×C4×C11—21no—
71C22×C4×C11—42no—
72C22×C4×C11—82no—
73C22×C4×C11—82no—
74C22×C4×C11C22⋊C412yes—
75C22×C4×C11C22×C411yescharacteristic
76C22×C4×C11C2×D411yescharacteristic
77C22×C4×C11C2×D411yescharacteristic
78C2×C8×C11—24no—
79C2×C8×C11—42no—
80C2×C8×C11—84no—
81C11×C4⋊C4—22no—
82C11×C4⋊C4—22no—
83C11×C22⋊C4—24no—
84C11×C22⋊C4—41no—
85C11×C22⋊C4—41no—
86C11×C22⋊C4—82no—
87C11×C22⋊C4—82no—
88C42×C11—21no—
89C42×C11—22no—
90C42×C11C2×C812yescomplemented
91C42×C11C2×D412yes—
92C42×C11#4112yes—
93#2972C2×C1111yescharacteristic, complemented
94#2328C2×C1111yescharacteristic
95#1478C2×C1112yescomplemented
96#1460C2×C1111yescharacteristic, complemented
97#1274C2×C1112yescomplemented
98C23×C11—22no—
99C23×C11—22no—
100C23×C11—22no—
101C23×C11—42no—
102C23×C11—42no—
103C23×C11—42no—
104C23×C11—42no—
105C23×C11—41no—
106C23×C11—41no—
107C23×C11C22⋊C814yes—
108C23×C11C2×C22⋊C411yescharacteristic
109D4×C11—24no—
110D4×C11—24no—
111D4×C11—24no—
112D4×C11—42no—
113D4×C11—88no—
114C2×C4×C11—22no—
115C2×C4×C11—22no—
116C2×C4×C11—41no—
117C2×C4×C11—41no—
118C2×C4×C11—44no—
119C2×C4×C11—41no—
120C2×C4×C11—41no—
121C2×C4×C11—42no—
122C2×C4×C11—41no—
123C2×C4×C11—41no—
124C2×C4×C11—42no—
125C2×C4×C11—41no—
126C2×C4×C11—41no—
127C2×C4×C11—82no—
128C2×C4×C11—84no—
129C2×C4×C11C4×D412yes—
130C2×C4×C11#12011yescharacteristic
131C2×C4×C11#12112yes—
132C2×C4×C11#12311yescharacteristic
133C2×C4×C11C22×C811yescharacteristic
134C2×C4×C11C2×M1611yescharacteristic
135C2×C4×C11#13112yes—
136C8×C11—44no—
137C8×C11—82no—
138C2×#127C4×C1111yescharacteristic
139C2×C4×D4C22×C1111yescharacteristic
140C2×C4×D4C22×C1111yescharacteristic
141C8×D4—24no—
142#431C22×C1112yes—
143#431C22×C1112yes—
144C2×C22⋊C8—22no—
145#390C4×C1111yescharacteristic
146#390C4×C1111yescharacteristic
147#386—22no—
148#386—22no—
149#382C4×C1111yescharacteristic
150#376C22×C1111yescharacteristic
151D4⋊C8—24no—
152#323—22no—
153C22×C11—21no—
154C22×C11—21no—
155C22×C11—24no—
156C22×C11—44no—
157C22×C11—44no—
158C22×C11—42no—
159C22×C11—42no—
160C22×C11—42no—
161C22×C11—82no—
162C22×C11—82no—
163C22×C11—81no—
164C22×C11—81no—
165C22×C11#38611yescharacteristic
166C22×C11C2×C22⋊C811yescharacteristic
167C22×C11#40811yescharacteristic
168C4×C11—22no—
169C4×C11—21no—
170C4×C11—21no—
171C4×C11—42no—
172C4×C11—42no—
173C4×C11—81no—
174C4×C11—81no—
175C4×C11C8×D412yes—
176C4×C11#43512yes—
177C22×D4—22no—
178C22×D4C2×C4×C1111yescharacteristic
179C22×D4C2×C4×C1111yescharacteristic
180C23×C4—21no—
181C23×C4D4×C1112yes—
182C22×C8—24no—
183#127—22no—
184#127C8×C1114yescomplemented
185C4×D4—22no—
186C4×D4—22no—
187C4×D4—22no—
188C4×D4—22no—
189C2×C4⋊C4C2×C4×C1111yescharacteristic
190C2×C4⋊C4C2×C4×C1111yescharacteristic
191C2×C22⋊C4—21no—
192C2×C22⋊C4—22no—
193C2×C22⋊C4—22no—
194C2×C22⋊C4D4×C1112yes—
195C2×C42C2×C4×C1111yescharacteristic
196C2×C42C2×C4×C1111yescharacteristic
197C2×C42C23×C1111yescharacteristic
198C4⋊C8—22no—
199C4⋊C8—22no—
200C22⋊C8—24no—
201C22⋊C8—22no—
202C22⋊C8—22no—
203C4×C8—22no—
204C4×C8D4×C1114yescomplemented
205#95—22no—
206#95—21no—
207#95—21no—
208C2×C11—21no—
209C2×C11—21no—
210C2×C11—44no—
211C2×C11—82no—
212C2×C11#186911yescharacteristic
213C2×C11#191011yescharacteristic
214C2×C11#191111yescharacteristic
215C24—21no—
216C24C11×C22⋊C412yes—
217C2×D4—28no—
218C2×D4—22no—
219C2×D4—22no—
220C2×D4—21no—
221C2×D4—22no—
222C2×D4—22no—
223C2×D4—82no—
224C2×D4—82no—
225C2×D4C2×C8×C1112yes—
226C2×D4C2×C8×C1112yescomplemented
227C2×D4C11×M1612yes—
228C22×C4—21no—
229C22×C4—22no—
230C22×C4—22no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—42no—
234C22×C4—82no—
235C22×C4—82no—
236C22×C4C11×C22⋊C412yes—
237C22×C4C22×C4×C1111yescharacteristic
238C22×C4C2×D4×C1111yescharacteristic
239C22×C4C2×D4×C1111yescharacteristic
240C2×C8—24no—
241C2×C8—42no—
242C2×C8—84no—
243C4⋊C4—22no—
244C4⋊C4—22no—
245C22⋊C4—24no—
246C22⋊C4—41no—
247C22⋊C4—41no—
248C22⋊C4—82no—
249C22⋊C4—82no—
250C42—21no—
251C42—22no—
252C42C2×C8×C1112yescomplemented
253C42C2×D4×C1112yes—
254C42C11×#4112yes—
255C11#910111yescharacteristic, direct product factor, Sylow
256C23—22no—
257C23—22no—
258C23—22no—
259C23—42no—
260C23—42no—
261C23—42no—
262C23—42no—
263C23—41no—
264C23—41no—
265C23C11×C22⋊C814yes—
266C23C2×C11×C22⋊C411yescharacteristic
267D4—24no—
268D4—24no—
269D4—24no—
270D4—42no—
271D4—88no—
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—44no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—42no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—42no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—82no—
286C2×C4—84no—
287C2×C4C4×D4×C1112yes—
288C2×C4C11×#12011yescharacteristic
289C2×C4C11×#12112yes—
290C2×C4C11×#12311yescharacteristic
291C2×C4C22×C8×C1111yescharacteristic
292C2×C4C2×C11×M1611yescharacteristic
293C2×C4C11×#13112yes—
294C8—44no—
295C8—82no—
296C22—21no—
297C22—21no—
298C22—24no—
299C22—44no—
300C22—44no—
301C22—42no—
302C22—42no—
303C22—42no—
304C22—82no—
305C22—82no—
306C22—81no—
307C22—81no—
308C22C11×#38611yescharacteristic
309C22C2×C11×C22⋊C811yescharacteristic
310C22C11×#40811yescharacteristic
311C4—22no—
312C4—21no—
313C4—21no—
314C4—42no—
315C4—42no—
316C4—81no—
317C4—81no—
318C4C8×D4×C1112yes—
319C4C11×#43512yes—
320C2—21no—
321C2—21no—
322C2—44no—
323C2—82no—
324C2C11×#186911yescharacteristic
325C2C11×#191011yescharacteristic
326C2C11×#191111yescharacteristic
subgroupG/H
center, socleC22×C11#386
commutatorC2×C4C22×C8×C11
Frattini, cosocleC2×C42C23×C11
prime radicalC2×C11×#127C4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C11×#2972C2semidirect
3. C11×#1478C2semidirect
4. C11×#1460C2semidirect
5. C11×#1274C2semidirect
28. C11×#127C8semidirect
48. C4×C8×C11D4semidirect
52. #9101C11direct (N × H)
64. C2×D4×C11C2×C8semidirect
90. C42×C11C2×C8semidirect
93. #2972C2×C11semidirect
95. #1478C2×C11semidirect
96. #1460C2×C11semidirect
97. #1274C2×C11semidirect
184. #127C8×C11semidirect
204. C4×C8D4×C11semidirect
226. C2×D4C2×C8×C11semidirect
252. C42C2×C8×C11semidirect
255. C11#9101direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C11×#29722
C11×#23282
C11×#14782
C11×#14602
C11×#12742
#910111